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QPages 12-14: Q24: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q24 Solution: A glass vessel measures exactly 10 cm _ 10 cm _ 10 cm at 0�C.…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently confuse the linear expansion coefficient of the glass vessel ($\alpha$) with its volumetric expansion coefficient ($\gamma$). Remember that for isotropic solids, the volumetric coefficient is approximately three times the linear coefficient ($\gamma_{glass} \approx 3\alpha$), so you must use $3 \times 6.5 \times 10^{-6}$ in the overflow equation.

A glass vessel measures exactly 10 cm _ 10 cm _ 10 cm at 0�C. It is filled completely with mercury at this temperature. When the temperature is raised to 10�C, 1.6 cm3^3 of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass = 6.5×10−6 �C−16.5 \times 10^{-6} \text{ �C}^{-1}.

Step-by-Step Verified Solution

**Answer:** γHg=1.81×10−4\gamma_{Hg} = 1.81 \times 10^{-4} /�C **Step-by-Step Explanation:** Glass vessel: 10×10×10=100010 \times 10 \times 10 = 1000 cm_ at 0�C. At 10�C, overflow = 1.6 cm_. ΔVoverflow=V0(γHg−γglass)ΔT\Delta V_{overflow} = V_0(\gamma_{Hg} - \gamma_{glass})\Delta T 1.6=1000(γHg−3×6.5×10−6)×101.6 = 1000(\gamma_{Hg} - 3 \times 6.5 \times 10^{-6}) \times 10 γHg−1.95×10−5=1.6×10−4\gamma_{Hg} - 1.95 \times 10^{-5} = 1.6 \times 10^{-4} γHg=1.795×10−4≈1.8×10−4\gamma_{Hg} = 1.795 \times 10^{-4} \approx 1.8 \times 10^{-4} /�C

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